Dr. Snow and Dr. Whitehead invested a Cholera outbreak in 19th century London and discovered that the disease spread through contaminated well water.

Epidemiology does not require specific knowledge of a disease. It studies interactions to learn how a disease spreads. It uses pattern analysis to understand how the environment, social networks, and infectious agents interact to cause an epidemic.

When Snow and Whitehead invested the Cholera outbreak, they did not understand what the disease was. This was the time before Germ Theory. The prevalant idea was Miasma Theory – diseases spread through bad smells. This wasn’t a terrible idea, as it associated smelly refuse with contamination. Indeed, many foul smells emitted by rotting meat and garbage are caused by bacteria and parasites.

19th Century Londoners lived in their filth and had poor sewage systems. Snow and Whitehead discovered Miasma Theory was irrelevant to the spread of cholera. They identified clusters where the disease broke out, mostly around Broad Street, where hundreds died.

Snow used pattern analysis. He used a street map and marked the locations where individuals were infected with cholera. This identified the cluster zones and the pattern in which the disease spread in the community. He created lists of possible infection vectors to explain the spread and eventually figured out that it was spread through well water.

The cholera outbreaks were centered around certain wells. The community would get the well water for drinking, cooking and cleaning, and that was how the disease spread. Snow and Whitehead closed the well and contained the outbreak.

It turns out that poor construction of the sewers and water systems in London created filty and polluted water. London, and later cities, rebuild their city water systems and prevented cholera and many other diseases.

Newer techniques allow us to refine their approach. Social Network theory offers new techniques for “mapping” social networks. This is useful for sexually spread diseases. Social Networks are “Scale-Free” and “Small-worlds” networks. Small worlds networks occur where any node is just a few steps from another random node. Scale Free networks follow power-law curves.

Epidemic Spreading in Scale-Free Networks (pdf)

The internet is a scale-free network and epidemiological techniques have been used to study computer viruses. Now, scientists can use computer models to study the spread of diseases across human social networks.

In this article, one of the findings is an epidemic threshold. If the disease does not cross this critical point, it dies out. If it crosses the threshold, it spreads and becomes a persistant epidemic. In a scale free network, even diseases with low infection rates can become prevalent. There are mathematical limitations on exponential epidemic growth in a scale-free network.

Social networks follow the power-law curve.
P(k)~k^-y
This measures the probability of a node connecting with a number of other nodes.
For most human networks, y= 2 to 3. (The internet is 2.5)

For instance, we can study the spread of sexual diseases by mapping out sexual contacts. A small number of nodes can have contacts with hundreds of other nodes. These are whores and sluts. A small number of other nodes have one or zero contacts. These are librarians and nuns. In between, the average nodes find an average of 3, or 4, or 5 contacts.

The disease can spread because of the nodes with a high number of contacts. However, we can also isolate these clusters to reduce their connections with the rest of the network.

There are some surprising (or not) findings when you apply this methodology to real world cases. AIDS is a more widespread epidemic in Africa than North America, yet Africans have fewer sexual partners than Americans. Americans, however, use safer sexual practices and have a lower rate of other sexual diseases that reduce their probability of contracting the disease in each encounter.

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